What is the slope of a line perpendicular to the x-axis?

2 Answers
Apr 30, 2018

Answer:

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Explanation:

the slope of a line parallel to the #x#-axis has slope #0#.

the slope of a line perpendicular to another will have a slope which is its negative reciprocal.

the negative reciprocal of a number is #-1# divided by the number (e.g. the negative reciprocal of #2# is #(-1)/2#, which is #-1/2#).

the negative reciprocal of #0# is #-1/0#.

this is undefined, since one cannot define the value of any number that is divided by #0#.

Jun 11, 2018

Answer:

We say vertical lines have "no slope," horizontal lines have zero slope. The equation is #x=text{constant}# so it's not equivalent to any slope-intercept form #y=mx+b.# The slope is undefined because the denominator, change in #x#, is zero.

Explanation:

One may use a direction vector, #(p,q),# instead of a slope. It's equivalent to a slope #q/p# but works when #p=0.# A line is expressed in parametric form: #(x,y)=(a,b)+t(p,q)# where #t# ranges over the reals. The parameter #t# forms a natural ruler along the line, each increment of one in #t# is a length #sqrt{p^2+q^2}# along the line.